Lee says the area element dS of a parametrised surface comes from the magnitude of the cross product of its tangent vectors. Is Lee right?

Circle one:   True   False

A flux computation comes out negative. What does the sign mean?

• More field flows against the chosen orientation
• The surface has zero area
• The field is zero everywhere
• The surface must be closed

What does the flux of a field through a surface measure?

• The net flow crossing the surface
• The area of the parameter domain
• The length of the boundary curve

What is the area element dS for a parametrised surface?

• The length of r sub u cross r sub v
• The dot product of r sub u with r sub v
• The sum of the two tangent vectors

The field F = (0, 0, 2) flows upward through the 3 by 4 rectangle in the plane z = 0. What is the upward flux?

Answer: ______________

Your flux setup reports an area of zero for a sphere with integrand 1. What is the likely fault?

• The sphere has no area
• The integrand 1 is illegal
• The normal or the parameter domain is wrong

Flipping the chosen normal changes the sign of the flux.

Circle one:   True   False

The flat unit square 0 <= x <= 1, 0 <= y <= 1 lies in the plane z = 0. The field F = (0, 0, 5) points straight up. What is the upward flux through the square?

Answer: ______________

Two students parametrise the same open surface with opposite normals and compare flux values. How should the numbers relate?

• They must be negatives of each other
• They must be identical
• One of them must be zero

A student dots the field with a tangent vector instead of the normal and calls it flux. What did they compute?

• The correct flux by a shortcut
• The surface area with a new formula
• Something else entirely, since flux needs the crossing direction